How to initialize the Invitation dialog (not the apprequest one)?

There are a lot of applications that use an Invitation dialog, like this one here:

However I find no documentation or a single topic describing this specific dialog. It is not the same as the apprequest dialog which is mostly referred to as the 'invitation dialog'.

That dialog is built with the FBML API. A good example can be found here. However this API is in process of deprecating.

With the new JavaScript SDK you can initialize an application invitation, using the Request Dialog.